Solution to Turunen’s open problems on n-fold filters

Article type: Research Article

Authors: Ma, Zhen Ming^*

Affiliations: School of Science, Linyi University, Linyi Shandong, P.R. China

Correspondence: [*] Corresponding author. Zhen Ming Ma, School of Science, Linyi University, Linyi Shandong, P.R. China. E-mail: [email protected].

Abstract: In this paper, we shall give answers to show that two open problems, which is proposed by Turunen et al. in (Erratum to:) n-Fold implicative basic logic is Gödel logic [Soft Computing 16(2012): 177–181,183]. That is, each n-fold positive implicative filter is an n-fold Boolean filter and in an n-fold fantastic BL-algebra, n-fold implicative basic logic and n-fold positive implicative basic logic coincide.

Keywords: Non-classical logics, BL-algebras, n-fold Boolean filters, n-fold positive implicative filters

DOI: 10.3233/IFS-151834

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1123-1126, 2016